PSI - Issue 35

Andreas Seupel et al. / Procedia Structural Integrity 35 (2022) 10–17 A. Seupel et al. / Procedia Structural Integrity 00 (2021) 000–000

13

4

tensile test

compression test

¯ u

¯ u

clamp

punch

domain of force

tensile specimen

measurement

ØD

strain gauges

domain of martensite measurement

H

TC 1

TC 2

Ød 1

l

compression specimen

clamp

h

TC 3

Ød 2

thermocouple

Fig. 1. Sketch of tensile and compression tests as implemented in the FE-program (symmetry utilized, displacement controlled). Dimensions: d 1 = 3.6 mm, l = 10.5 mm, H = 200 mm, D = 60 mm, d 2 = 6 mm, h = 3 mm. All dimensions of tensile test can be found in Pru¨ger et al. (2014). Convective boundary conditions with heat transfer coe ffi cient h t are applied on all free boundaries (constant environmental temperature). Gap conductance with coe ffi cient h c is applied between punch and compression specimen. The prefactor L especially distinguishes between uni-axial tension (cos 3 φ = 1), uni-axial compression (cos 3 φ = − 1) and pure shear (cos 3 φ = 0). The parameter b 0 determines the magnitude of asymmetry which vanishes for temperatures ϑ ϑ b0 and additionally changes during martensite evolution ( · – Macauly-brackets). In accordance with experimental results on TRIP-steels of Kulawinski et al. (2015) the initial yield stress is not a ff ected by the Lode-angle. The model has been implemented into the FE-program ABAQUS / Std. as user defined material routine (UMAT). Coupled thermomechanical simulations are performed solving the transient heat equation

ρ c ˙ ϑ = λ th ∆ x ϑ + ησ eq ˙ ε eq ∀

#» x ∈ B ,

(12)

with constant specific heat capacity c , constant thermal conductivity λ th and density ρ . The plastic dissipation is assumed as heat source. The Taylor-Quinney-coe ffi cient is chosen as η = 1, i.e., full dissipation of inelastic processes, according to literature findings which report even values η > 1 due to extra contribution of the martensitic transition, see Zaera et al. (2013).

3. Material

The model is applied to experimental results of the initially fully austenitic cast steel X3CrMnNi 16-6-6 which has extensively been characterized by Wolf (2012). The material exhibits the curve-crossing-e ff ect in both tension and compression, see Pru¨ger et al. (2014); Wolf et al. (2014). The parameters α oc ( ϑ, h ), β oc ( ϑ, h ) and n oc of the martensite evolution law can be found in (Seupel et al., 2020, Section 22.4.2.1). Quasi-static tensile and compression tests have been performed at di ff erent environmental temperatures. Additionally, uni-axial tests have been conducted at higher technical strain rates for constant environmental temperature of 293 K. Stress-strain-curves and the evolution of α - martensite are extracted from all the tests. The thermomechanically coupled simulations of tensile and compression tests are conducted for ϑ = 293 K in order to demonstrate the capability of the model to predict the curve-crossing-